Automorphic compatible systems of Galois representations

Thesis

This thesis investigates properties of compatible systems of Galois representations, mainly focusing on the compatible systems which are attached to certain classes of automorphic representations of GL_n.

We develop a general method to prove independence results for algebraic monodromy groups in abstract compatible systems of representations, and give applications both in characteristic zero and in positive characteristic settings. In the case of automorphic compatible systems (and actually for a slightly larger class of geometric compatible systems), we apply our method to deduce an independence result, assuming a classical irreducibility conjecture. In addition, we also deduce an independence result in the case of compatible systems of lisse sheaves on normal varieties over finite fields.

We then focus on the study of the geometry of (pseudo)deformation spaces of Galois representations and definite unitary groups eigenvarieties at points corresponding to certain classical automorphic representations. In this context, we present smoothness results known in the literature, and suggest possible implications for automorphic compatible systems.

Authors: Guidi, F

• DOI: 10.5287/ora-2axwgkmz0
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford